Find the linearization L(r. y, 2) of the function f(r, y. 2) = y² sin(2rz) at Po = (7,2.4). Then find an upper bound for the magnitude of the error E in the approximation f(r, y, z) L(r, y, z) over the region R. ro5- R: Ir-피S0.2, ly-2 < 0.3, 13-1s0.1

Q: Calculate dw/du and dwldv using the following functions: = f(x, y, z) = 3x² – 2ry + 4z2 = x(u, v) =…

A: Apply chain rule

Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: Given f(x,y)=ln(x^2+y^2) a) determine Dv f(2,3) with v = b) what is the angle, in radians, between…

A:

Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

A:

Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

A:

Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

A:

Q: Find an equation of the tangent plane at P = (0, 3, – 1) to the sur- face with equation ze* + ez+1 =…

A:

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Q\ Let F(x,y,z)=(sin(xy), e",2x+yz") then find: 1. Grad F(x,y,z) at (-1,1,-1) 2. Div F(x,y,z) at…

A:

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

A:

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: Evaluate / = F dr where F [y+z, z+x, x+y] and C: r(t)= [t, sint, cost], from A:(0, 0, 1) to B:(T, 0,…

A: Answer

Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

A:

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: | (xy dx + 2y dy)

A:

Q: Let the curve C be the line segment from (0, 0) to (3, 1). Let F = ⟨2x-y, 4y-x⟩ Calculate the…

A:

Q: | 5y? dx +xy dy

A:

Q: (a) Let R be a rectangular region bounded by the lines x = -1, x = 2, y = 0, and y = 2. Find: ²y dx…

A:

Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

A:

Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

A: